Question

74\. In \(2010,3.30 \times 10^{9}\) gallons of gasoline were consumed in the United States. The following assumptions can be made: Gasoline is mainly n-octane, \(\mathrm{C}_{8} \mathrm{H}_{18}(d=0.7028 \mathrm{~g} / \mathrm{mL})\) Burning one mole of n-octane in oxygen releases 5564.2 \(\mathrm{kJ}\) of heat. The heat capacity \(C\) of the surface region of the earth is \(2.6 \times 10^{23} \mathrm{~J} / \mathrm{K}\) What is the increase in temperature of the surface region of the earth due to gasoline consumption in the United States?

Short answer

Answer: The surface temperature of the Earth would increase by 0.0000164 degrees Celsius.

Step-by-step solution

Convert gallons of gasoline to moles of n-octane.

First, convert gallons of gasoline to mL. There are approximately 3785 mL in a gallon, so the total amount of gasoline in 2010 was \(3.30 \times 10^{9}\) gallons x 3785 mL/gallon = \(1.24805 \times 10^{14}\) mL. Using the density of n-octane (\(0.7028 g/mL\)), we can calculate the total mass of n-octane used: \(1.24805 \times 10^{14}\) mL x \(0.7028 g/mL\) = \(8.7726 \times 10^{13}\) g. Then, using the molar mass of n-octane (\(114.22 g/mol\)), convert this into moles: \(8.7726 \times 10^{13}\) g / \(114.22 g/mol\) = \(7.6785 \times 10^{11}\) moles.

Calculate total heat produced.

Next, calculate the total heat by multiplying the number of moles burned by the heat produced per mole: \(7.6785 \times 10^{11}\) moles x \(5564.2 kJ/mol\) = \(4.27 \times 10^{15} kJ\). Because the heat capacity is in Joules, convert the energy to Joules: \(4.27 \times 10^{15} kJ \times 10^{3}J/kJ\) = \(4.27 \times 10^{18} J\).

Calculate the temperature increase.

Finally, find the temperature increase by dividing the total energy by the heat capacity of the surface Earth: \((4.27 \times 10^{18} J) / (2.6 \times 10^{23} J/K) = 1.64 \times 10^{-5} K\). So, assuming all that energy were to go into heating the surface of the Earth, the surface temperature would increase by \(1.64 \times 10^{-5}\) K, or 0.0000164 degrees Celsius due to gasoline combustion in the United States in 2010.

Key concepts

Calculation of Energy from Combustion

The calculation of energy from the combustion of fuels like gasoline is an essential aspect of environmental chemistry, as it allows us to understand the energy release and its potential environmental impact. When a fuel combusts, it reacts with oxygen to produce energy in the form of heat. The released energy is quantified as the enthalpy change, typically measured in kilojoules per mole (kJ/mol).

To calculate the total energy released from burning gasoline, one would need to know the amount of fuel combusted and the energy released per mole of fuel. In our example, by using the molar heat of combustion for n-octane, which is 5564.2 kJ/mol, and the total number of moles of n-octane combusted, we can deduce the total energy output. Multiplying the number of moles by the energy released per mole gives us the total energy released in kilojoules. To fully understand the magnitude of this energy release, it is often useful to also convert this energy to more familiar units, such as joules.

Converting Gallons to Moles

The process of converting gallons to moles is a two-step exercise that involves unit conversion and application of chemical principles. Starting with a known volume of a liquid fuel, like gasoline, we can use its density to first convert that volume to mass and then the molar mass to turn that figure into moles.

To facilitate this conversion, you'll need the density of the substance in question and its molar mass. For n-octane, we use a density of 0.7028 grams per milliliter (g/mL) and a molar mass of 114.22 grams per mole (g/mol). This calculation hinges on understanding the relationship between mass, volume, and moles: volume (in mL) times density equals mass, followed by mass divided by molar mass equals moles.

Enthalpy Changes in Chemical Reactions

Enthalpy change, denoted by \( \Delta H \), is the measure of heat absorbed or released during a chemical reaction at constant pressure. In the context of gasoline combustion, it represents the energy released when octane reacts with oxygen in the air to produce carbon dioxide and water. A negative \( \Delta H \), as observed in exothermic reactions like combustion, indicates that energy is being released.

The significance of \( \Delta H \) lies in its ability to convey the energy implications of a reaction. It is fundamental in predicting the potential effects that such a reaction can have on the environment. In our scenario, calculating the enthalpy changes helps estimate how much energy is injected into the Earth’s atmosphere and surface, which directly relates to environmental concerns like global warming and climate change.

Application of Heat Capacity in Environmental Chemistry

Heat capacity, often represented by \( C \), is a physical property of matter that indicates how much heat energy is required to raise the temperature of a given mass by one degree Celsius. It plays a vital role in environmental chemistry by helping us predict how energy changes in the environment, such as those from combustion, might affect the temperature of the Earth.

The concept of heat capacity allows scientists and learners to calculate the effect of energy release on the Earth's surface temperature. By dividing the total energy added to the environment by the Earth's heat capacity, we can estimate the resulting temperature increase. This is of particular importance in understanding the thermal balance of the Earth and the potential for human activities, like burning fossil fuels, to disrupt it. Knowledge of heat capacity and its application thus contributes to analyzing and mitigating the environmental consequences of energy use.